Finite Group DatabasebetaFinite Group Databasebeta| order | 1194 |
| isoclinism | isoclinic class of D199⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | D199⋊C3 |
| unambiguous semidirect product | (C199⋊C3)⋊C2 |
| Fitting, socle, derived, Sylow | C199 ⋊ C2×C3 |
| Hall | C199⋊C3 ⋊ C2 |
| Hall | D199 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C199 | C2×C3 |
| LCS | G ▷ C199 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 199 |
| transitive degree | μt(G) = 199 |
Polycyclic presentation:
2,3,199|c^a=c^198,c^b=c^10639 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D199⋊C3, #13184226⋊C2, C3×D199⋊C3, … |
| maximal normal subgroup of | C2×D199⋊C3, #13184226⋊C2, C3×D199⋊C3, … |
| maximal quotient of | (C199⋊C3)⋊C4, C2×D199⋊C3, #13184224⋊C2, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1194, 1);